Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}2x+5y &= -1 \\ 2x+9y &= 3\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $9y = -2x+3$ Divide both sides by $9$ to isolate $y$ $y = {-\dfrac{2}{9}x + \dfrac{1}{3}}$ Substitute this expression for $y$ in the first equation. $2x+5({-\dfrac{2}{9}x + \dfrac{1}{3}}) = -1$ $2x - \dfrac{10}{9}x + \dfrac{5}{3} = -1$ Simplify by combining terms, then solve for $x$ $\dfrac{8}{9}x + \dfrac{5}{3} = -1$ $\dfrac{8}{9}x = -\dfrac{8}{3}$ $x = -3$ Substitute $-3$ for $x$ back into the top equation. $2( -3)+5y = -1$ $-6+5y = -1$ $5y = 5$ $y = 1$ The solution is $\enspace x = -3, \enspace y = 1$.